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Excel in math and science
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Absolute Value
Absolute value is a mathematician's way of judging numbers by their magnitude rather than their positive/negative value. It is the distance of the number from 0 on a number line.
Excel in math and science
Master concepts by solving fun, challenging problems.
It's hard to learn from lectures and videos
Learn more effectively through short, conceptual quizzes.
Our wiki is made for math and science
Master advanced concepts through explanations,
examples, and problems from the community.
Used and loved by 4 million people
Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.
Concept Quizzes
Let \(x=70\) be one root of the equation \(2\lvert x-10\rvert=x+a,\) where \(a\) is a constant. Then what is the other root?
Excel in math and science
Master concepts by solving fun, challenging problems.
It's hard to learn from lectures and videos
Learn more effectively through short, conceptual quizzes.
Our wiki is made for math and science
Master advanced concepts through explanations,
examples, and problems from the community.
Used and loved by 4 million people
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Let \(S\) be the solution set of the equation \(\lvert 2x-1 \rvert + 3\lvert x-29\rvert=5x-88.\) Then what is \(S?\)
Excel in math and science
Master concepts by solving fun, challenging problems.
It's hard to learn from lectures and videos
Learn more effectively through short, conceptual quizzes.
Our wiki is made for math and science
Master advanced concepts through explanations,
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Used and loved by 4 million people
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How many ordered pairs \((x, y)\) are there such that \(x\) is a nonzero integer that satisfies \(-8\leq x \leq 8\), \(y\) is a nonzero integer that satisfies \(-2\leq y \leq 2\), and \[\lvert x+y \rvert = \lvert x \rvert + \lvert y \rvert?\]
Details and assumptions
For an ordered pair of integers \((a,b)\), the order of the integers matter. The ordered pair \((1, 2)\) is different from the ordered pair \((2,1) \).
Excel in math and science
Master concepts by solving fun, challenging problems.
It's hard to learn from lectures and videos
Learn more effectively through short, conceptual quizzes.
Our wiki is made for math and science
Master advanced concepts through explanations,
examples, and problems from the community.
Used and loved by 4 million people
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How many ordered triples of integers \( (a, b, c) \) subject to \( -20 < a < b < c < 20,\) are there, such that
\[ \left| a + b + c \right | = |a| + |b| + |c|? \]
Excel in math and science
Master concepts by solving fun, challenging problems.
It's hard to learn from lectures and videos
Learn more effectively through short, conceptual quizzes.
Our wiki is made for math and science
Master advanced concepts through explanations,
examples, and problems from the community.
Used and loved by 4 million people
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including olympiad champions, researchers, and professionals.
If \(20 < a \leq 21\), what is the value of \[ \bigg| 2-a- \big| 6- \lvert a-20 \rvert \big| \bigg| ?\]